How To Choose The Fastest Supermarket Line?

How often do you find yourself in the fastest supermarket line? I bet that it does not happen often. On a recent supermarket trip, I noticed someone eyeing a faster-moving parallel line. Soon after, the person switched to that queue, only to move even slower.

Why does this happen? Are we inherently bad at choosing supermarket checkout lines? In this essay, this is the first set questions I will be addressing. Following this, I will dive into the origins of queueing theory, a technical field that studies such systems.

Finally, we will look at a strategy that lets us choose the fastest supermarket line. This solution is surprisingly counter-intuitive. Without any further ado, let us begin.

This essay is supported by Generatebg

Why is it So Hard to Choose the Fastest Supermarket Line?

The first point that I would like to explicitly address is the fact that what you experience is not an illusion. It is actually hard to choose the fastest supermarket line. To understand why, let us imagine a hypothetical supermarket with three billing counters: A, B, and C.

As we all know and have experienced, there could be multiple reasons for any of these counters to be bottle-necking. For example, one of the counters could be operated by new or incompetent staff, or an old person might be taking her time picking pennies from her purse to pay, or there might be a dispute about a defective product right at the counter.

Let us say that we do not know what is about to happen in advance (if we did, we’d be able to choose the faster line, isn’t it?). So, we can assume that the fastest checkout queue at any given point is a random one: A or B or C.

If that’s the case, the following is the range of possibilities for ranking checkout counters based on speed of processing (fastest to slowest):

Now, suppose that you just happened to be in the line to counter ‘C’. Given the range of permutations, it is only two out of six times (2/6) that you are in the fastest moving line. In other words, your chances of picking the fastest moving supermarket line is 1/3.

When we combine these low odds with the innate human bias towards negativity (this is why your local news channel reports more on negative events than positive events), we see why we feel that it is so hard to choose the fastest supermarket line. But as it turns out, this problem extends beyond just supermarkets.

The Origins of Queueing Theory

In the early 1900s, a Danish engineer named Agner Krarup Erlang, while was working for Copenhagen telephone exchange, asked the following question:

How many main telephone lines (trunk lines) do we need to handle all the phone calls in a town?

Imagine each checkout counter operator as a telephone trunk line and each supermarket customer as an individual telephone call request. If we provided each telephone with its own trunk line, it would be massively inefficient because most phones are not constantly used.

On the other hand, if we provided just one trunk line for the entire town, then it would cause outrageously long waiting times since the rest of the town’s callers would be waiting for one person to complete at a time. The answer, then, lies somewhere in the middle.

Erlang modelled the number of incoming telephone calls using a Poisson distribution and solved the problem assuming deterministic call behaviour. Although this was not a realistic assumption, his paper and initial work kickstarted what is known today as queueing theory.

Fast forward to today, this field has applications ranging from how computer processors process requests to how manufacturing companies improve production efficiency on assembly lines. All this is fascinating. But what about our supermarket problem? Right; let’s get back to that.

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How to Choose the Fastest Supermarket Line?

You might think that the method to choose the fastest supermarket line would be some sort of optimisation algorithm to balance the ratio of the number of open billing counters to the number of waiting customers.

But rather counter-intuitively, the queue is at its fastest when we remove the element of choice altogether. That sounds crazy, right? But bear with me; this will make sense.

Let us go back to the situation where one of the counters (say, B) is bottle-necked by some random event. On this occasion, the customers in the B-line have to wait. Instead, imagine a system where there is a single line that feeds into all three counters.

In such a system, each customer gets the first free counter out of the three. When a counter experiences a random bottleneck, there are no customers waiting in line for that counter to speed up. This system is (theoretically) around 3 times as efficient as the previous system.

You might have already experienced this kind of a queueing system at airport security lines and other places. However, I have not often seen this system used in supermarkets. Why is that?

The Challenges of Speed Vs. Psychology

The issue with such a system is that it places a negative psychological load on the customers waiting in line. A single queue robs people of the sense of freedom of choice. So, in another plot twist, people prefer a sense of (arguably elusive) choice over efficiency when it comes to supermarket queues.

In fact, queueing theory models these inefficiencies using the following technical terms:

Balking: Customers see a long line and decide not to join.

Jockeying: Customers switch lines if they think that there is a faster line.

Reneging: Customers leave the line if they feel that they have waited too long.

As for airports, the security authorities do not have much incentive to offer the most flawless and friendly customer experience to travelers. Their prime goal is to process travelers as fast and efficiently as possible.

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Final Comments

We might have had an interesting discussion about queueing theory and a hypothetically faster queueing method. However, given the realistic conditions at your neighbourhood supermarket, we still do not have any clear method that lets you choose the fastest line.

So, what should you do? Well, let us refer back to our mathematics based on permutations. Assuming random conditions, you just have a probability of 1/3 that you will choose the fastest-moving line. This means that most of the time, you will be moving slowly.

But the bright side is that you can expect to choose the fastest line on one-third of your supermarket visits. That might be a consoling thought. However, there is something even better.

The latest supermarket billing systems have gotten rid of the human cashier and have automated self-service billing counters. I have noticed that such systems implement a single queue system similar to airport security.

So, if you have a choice between a billing system with a cashier and without a cashier, choosing the one without a cashier gives you the best chance of choosing the fastest supermarket line!

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Further reading that might interest you:

• How To Really Make Sense Of Hotelling’s Law?
• Learning Better Using Tacit Knowledge.
• How To Really Understand Gruen Effect?

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